(Reuters) - In a move viewed skeptically by legal experts, the socially conservative chief justice of Alabama's Supreme Court on Tuesday encouraged judges in his state to ignore a federal ruling last week striking down its ban on gay marriage.

Justice Roy Moore, in a letter addressed to Alabama Governor Robert Bentley, said Friday's federal ruling, which was put on hold for two weeks and could be superseded by a U.S. Supreme Court decision on gay marriage due by the end of June, violates the state constitution.

"I am dismayed by those judges in our state who have stated they will recognize and unilaterally enforce a federal court decision which does not bind them," Moore wrote. "I would advise them that the issuance of such licenses would be in defiance of the laws and constitution of Alabama."

Ronald Krotoszynski, a constitutional law expert at the University of Alabama School of Law, said Moore's words carry little legal weight, as federal constitutional law trumps that of states.

"There is no credible legal argument that an order from a federal judge with jurisdiction over a matter isn't binding on a state government," he said.

Moore has long been a lightning rod. In 2000, he gained national attention for installing a Ten Commandments monument in the state's judicial building. He was removed from office three years later after defying a federal order to take it down and was returned to his post by voters in 2012.

U.S. District Court Judge Callie Granade, an appointee of President George W. Bush, whose ruling struck down the state's gay marriage ban as unconstitutional, issued a second ruling on Tuesday awarding a separate Alabama same-sex couple the right to marry.

State Representative Patricia Todd, a Democrat who is the state's sole gay lawmaker, threatened over the weekend to expose her colleagues' extramarital affairs if they continue to cite "family values" while speaking against the ruling.

Bentley, a Republican, said in a statement put out after Moore's letter that he supports Alabama's gay marriage ban and will work to uphold it.

Gay rights activists were critical of Moore's letter.

"There's something deeply ironic about a judge seeking the right to ignore another judge's ruling while crying 'judicial activism,'" the Human Rights Campaign's Alabama director, Ashley Jackson, said in a statement.

(Reporting by Jonathan Kaminsky in New Orleans; Editing by Eric Beech)